Projected free fall trajectories

How we manage to reconstruct the three-dimensional character of the world from the two-dimensional representations on our retinae has been a lively subject of research in the last ten or fifteen years. One principle that has emerged unifying many of these ideas is the need for constraints to allow the visual system to interpret the images it receives as three-dimensional. These constraints come from assumptions about the nature of the situation that produced the image. We have looked at how gravity can be used as a constraint in the case of a free fall trajectory projected onto an image plane by central projection. We have examined several possible methods for deriving the initial conditions of the trajectory from the two-dimensional projection, and examined their behavior under noisy and noiseless conditions, using both image simulations and videotapes of a real ball. We show that there are several ways to robustly compute the initial conditions of the parabolic trajectory from the image data in the presence of noise.     

Interactive computer graphics in the study of human body planar motion under free fall conditions

A computer program utilizing interactive graphics was developed in order to study the planar motion of a five-segment model of the human body. By providing instantaneous feedback and convenient graphical representation of the body, the program allows the user to quickly simulate and study body motions of interest. Consequently, the model is a useful tool for the researcher and may be readily employed for student instructional purposes.The configuration of the model, and the derivation and validation of the equations of motion, are included. Several options provided by the simulation are described.     

Projected Loss of a Salamander Diversity Hotspot as a Consequence of Projected Global Climate Change

Background

Significant shifts in climate are considered a threat to plants and animals with significant physiological limitations and limited dispersal abilities. The southern Appalachian Mountains are a global hotspot for plethodontid salamander diversity. Plethodontids are lungless ectotherms, so their ecology is strongly governed by temperature and precipitation. Many plethodontid species in southern Appalachia exist in high elevation habitats that may be at or near their thermal maxima, and may also have limited dispersal abilities across warmer valley bottoms.

Methodology/Principal Findings

We used a maximum-entropy approach (program Maxent) to model the suitable climatic habitat of 41 plethodontid salamander species inhabiting the Appalachian Highlands region (33 individual species and eight species included within two species complexes). We evaluated the relative change in suitable climatic habitat for these species in the Appalachian Highlands from the current climate to the years 2020, 2050, and 2080, using both the HADCM3 and the CGCM3 models, each under low and high CO₂ scenarios, and using two-model thresholds levels (relative suitability thresholds for determining suitable/unsuitable range), for a total of 8 scenarios per species.

Conclusion/Significance

While models differed slightly, every scenario projected significant declines in suitable habitat within the Appalachian Highlands as early as 2020. Species with more southern ranges and with smaller ranges had larger projected habitat loss. Despite significant differences in projected precipitation changes to the region, projections did not differ significantly between global circulation models. CO₂ emissions scenario and model threshold had small effects on projected habitat loss by 2020, but did not affect longer-term projections. Results of this study indicate that choice of model threshold and CO₂ emissions scenario affect short-term projected shifts in climatic distributions of species; however, these factors and choice of global circulation model have relatively small affects on what is significant projected loss of habitat for many salamander species that currently occupy the Appalachian Highlands.     

Optimal javelin trajectories

A companion paper has treated computer simulation of javelin flight using measured lift, drag and pitching moments. In the present paper we present, categorize and discuss the relative significance of various initial conditions in such a simulation. Since the differential equations describing flight are autonomous, the eventual javelin range and entry angle are unique functions of the initial conditions. A series of successively less constrained optimum solutions is defined, the last of which is the global optimum javelin trajectory. Sensitivities of these trajectories to perturbations from the optima and their implications for throwers are discussed. Finally, we investigate the effects of some design and environmental parameters on optimal initial conditions and trajectories.     

Optimal discus trajectories

A general 3-D dynamic model for men's and women's discus flight is presented including precession of spin angular momentum induced by aerodynamic pitching moment. Dependence of pitching moment coefficient on angle of attack is estimated from experiment. Numerical integration of 11 equations of motion for nominal release speed v₀=25 m/s and axial spin p₀=42 rad/s also requires 3 other release conditions; initial discus flight path angle β₀, pitch attitude θ₀, and roll angle φ₀. Optimal values for these release conditions are calculated iteratively to maximize range and are similar for both men and women. The optimal men's trajectory and range R=69.39 m is produced by the strategy β₀=38.4°, θ₀=30.7°, and φ₀=54.4°. Initial angular velocities except spin are chosen to minimize wobble but an optimal initial spin rate p₀=25.2 rad/s exists that also maximizes range. Optimal 3-D range exceeds that predicted by 2-D models because, although angle of attack and lift are negative initially, 3-D motion allows advantageous orientation of lift later in flight, with tilt of the axis of symmetry from vertical becoming much smaller at landing. Optimal strategies are discontinuous with wind speed, resulting in slicing and kiting strategies in large head and tail winds, respectively. Sensitivity of optimal range is largest to initial β₀ and least to φ₀. Present calculations do not account for dependence of initial release angle or spin on release velocity or among other release conditions.     

Three dimensional arm trajectories

Biological Cybernetics - Planar arm trajectories are characterized by a segmentation of the hand velocity profile and by a coupling between shape and speed. The question addressed in this paper is...     

Projected estimates of cancer in Canada in 2022

Background:Regular cancer surveillance is crucial for understanding where progress is being made and where more must be done. We sought to provide an overview of the expected burden of cancer in Canada in 2022.Methods:We obtained data on new cancer incidence from the National Cancer Incidence Reporting System (1984–1991) and Canadian Cancer Registry (1992–2018). Mortality data (1984–2019) were obtained from the Canadian Vital Statistics — Death Database. We projected cancer incidence and mortality counts and rates to 2022 for 22 cancer types by sex and province or territory. Rates were age standardized to the 2011 Canadian standard population.Results:An estimated 233 900 new cancer cases and 85 100 cancer deaths are expected in Canada in 2022. We expect the most commonly diagnosed cancers to be lung overall (30 000), breast in females (28 600) and prostate in males (24 600). We also expect lung cancer to be the leading cause of cancer death, accounting for 24.3% of all cancer deaths, followed by colorectal (11.0%), pancreatic (6.7%) and breast cancers (6.5%). Incidence and mortality rates are generally expected to be higher in the eastern provinces of Canada than the western provinces.Interpretation:Although overall cancer rates are declining, the number of cases and deaths continues to climb, owing to population growth and the aging population. The projected high burden of lung cancer indicates a need for increased tobacco control and improvements in early detection and treatment. Success in breast and colorectal cancer screening and treatment likely account for the continued decline in their burden. The limited progress in early detection and new treatments for pancreatic cancer explains why it is expected to be the third leading cause of cancer death in Canada.

The impact of cancer on the Canadian population and health care systems is substantial. Cancer is the leading cause of death in Canada^1,2 and previous estimates have shown that 43% of all people in Canada are expected to receive a cancer diagnosis in their lifetime.³ With an aging and growing population, the number of new cancer cases and deaths in Canada is also increasing.⁴ In addition to its impact on health, cancer is costly. The economic burden of cancer care in Canada rose from $2.9 billion in 2005 to $7.5 billion in 2012, annually.⁵Given the considerable health and economic impact of cancer in Canada, comprehensive and reliable surveillance information is necessary for identifying where progress has been made and where more attention and resources are needed. To meet these needs, the Canadian Cancer Statistics Advisory Committee, in collaboration with the Canadian Cancer Society, Statistics Canada and the Public Health Agency of Canada, produces the latest surveillance statistics on cancer in Canada.Cancer data often lag the current date by several years, owing to the time associated with collecting, verifying and analyzing the data. Short-term cancer incidence and mortality rates can be projected by extrapolating past trends to estimate future trends, using statistical models. These short-term projections provide a more up-to-date estimate of the cancer landscape in Canada. Incidence and mortality counts, along with age-standardized rates, provide a picture of the impact of cancer in Canada, which is essential for resource planning, research and informing cancer-control programs.Canadian Cancer Statistics 2021³ provided detailed estimates of cancer incidence, mortality and survival in Canada by age, sex, geographic region and over time for 22 cancer types.³ Here, we provide updated estimates of the counts and age-standardized rates of new cancer cases (incidence) and cancer deaths (mortality) expected in 2022 by sex and province and territory, for all ages combined.     

Projected climate‐driven faunal movement routes

Historically, many species moved great distances as climates changed. However, modern movements will be limited by the patterns of human‐dominated landscapes. Here, we use a combination of projected climate‐driven shifts in the distributions of 2903 vertebrate species, estimated current human impacts on the landscape, and movement models, to determine through which areas in the western hemisphere species will likely need to move to track suitable climates. Our results reveal areas with projected high densities of climate‐driven movements – including, the Amazon Basin, the southeastern United States and southeastern Brazil. Some of these regions, such as southern Bolivia and northern Paraguay, contain relatively intact landscapes, whereas others such as the southeastern United States and Brazil are heavily impacted by human activities. Thus, these results highlight both critical areas for protecting lands that will foster movement, and barriers where human land‐use activities will likely impede climate‐driven shifts in species distributions.     

Dynamics of Vaccination Strategies via Projected Dynamical Systems

Previous game theoretical analyses of vaccinating behaviour have underscored the strategic interaction between individuals attempting to maximise their health states, in situations where an individual's health state depends upon the vaccination decisions of others due to the presence of herd immunity. Here, we extend such analyses by applying the theories of variational inequalities (VI) and projected dynamical systems (PDS) to vaccination games. A PDS provides a dynamics that gives the conditions for existence, uniqueness and stability properties of Nash equilibria. In this paper, it is used to analyse the dynamics of vaccinating behaviour in a population consisting of distinct social groups, where each group has different perceptions of vaccine and disease risks. In particular, we study populations with two groups, where the size of one group is strictly larger than the size of the other group (a majority/minority population). We find that a population with a vaccine-inclined majority group and a vaccine-averse minority group exhibits higher average vaccine coverage than the corresponding homogeneous population, when the vaccine is perceived as being risky relative to the disease. Our model also reproduces a feature of real populations: In certain parameter regimes, it is possible to have a majority group adopting high vaccination rates and simultaneously a vaccine-averse minority group adopting low vaccination rates. Moreover, we find that minority groups will tend to exhibit more extreme changes in vaccinating behaviour for a given change in risk perception, in comparison to majority groups. These results emphasise the important role played by social heterogeneity in vaccination behaviour, while also highlighting the valuable role that can be played by PDS and VI in mathematical epidemiology.     

Projected Lifetime Healthcare Costs Associated with HIV Infection

Objective

Estimates of healthcare costs associated with HIV infection would provide valuable insight for evaluating the cost-effectiveness of possible prevention interventions. We evaluate the additional lifetime healthcare cost incurred due to living with HIV.

Methods

We used a stochastic computer simulation model to project the distribution of lifetime outcomes and costs of men-who-have-sex-with-men (MSM) infected with HIV in 2013 aged 30, over 10,000 simulations. We assumed a resource-rich setting with no loss to follow-up, and that standards and costs of healthcare management remain as now.

Results

Based on a median (interquartile range) life expectancy of 71.5 (45.0–81.5) years for MSM in such a setting, the estimated mean lifetime cost of treating one person was £360,800 ($567,000 or €480,000). With 3.5% discounting, it was £185,200 ($291,000 or €246,000). The largest proportion (68%) of these costs was attributed to antiretroviral drugs. If patented drugs are replaced by generic versions (at 20% cost of patented prices), estimated mean lifetime costs reduced to £179,000 ($281,000 or €238,000) and £101,200 ($158,900 or €134,600) discounted.

Conclusions

If 3,000 MSM had been infected in 2013, then future lifetime costs relating to HIV care is likely to be in excess of £1 billion. It is imperative for investment into prevention programmes to be continued or scaled-up in settings with good access to HIV care services. Costs would be reduced considerably with use of generic antiretroviral drugs.